OK, but do you believe the rich man is actually in Hades as Jesus tells the story? If so, there is a bit of a challenge since the rich man characterizes his state as being "in agony in flames".
It's a parable, so "actually" is a bit odd. But yes.
I trust you see the problem: How could the final judgment be any worse for him than being in agony in flames? If, on the other hand, this waiting state is one in which he is simply waiting - and not roasting - then, you could make the case that it is a waiting state. But the Luke 16 account does have the rich man in real torment.
No, I don't see the problem. He's in agony in Hades, the intermediate state. He'll be destroyed in the final judgement.
I checked three commentaries on Luke. The Word commentary explicitly called it temporary. Hermeneia refers to a more explicit treatment in connection with 8:30, which calls it temporary. The Anchor Bible distinguishes it from Gehenna, but says it's far from certain.
TDNT has an article on Hades (to which the Anchor Bible refers). It portrays the usual understanding, which is that originally Sheol was everyone's destination. But in NT times several concepts coexisted. One was separation of Sheol / Hades into two parts, for saved and not. Another had the saved go immediately to Paradise, and then be resurrected in a general resurrection. They see Luke 16:23 as reflecting the first, and Luke 23:43 the second. Of course this may just be an issue of terminology, since one could certainly say that paradise was simply a term for the good part of Hades.
"In respect of the duration of this sojourn, there can be no doubt that it was originally thought to be everlasting (→ n. 2). Independently of the changes in the conception of Hades mentioned, this view lived on where only a partial doctrine of the resurrection was taught.[their references are to Jewish documents outside the NT] On the other hand, where a general resurrection was expected, the stay in Hades was thought to be limited in time, as everywhere in the NT. The fact that there were these different views as to which souls are in Hades, and for how long, meant that there were great variations on this question in the Judaism of NT days."
"Finally, the NT agrees that the stay in Hades is limited, as may be seen from the sharp distinction between ᾅδης and γέεννα. Throughout the NT Hades serves only an interim purpose. It receives souls after death,14 and delivers them up again at the resurrection (Rev. 20:13). The resurrection constitutes its end (20:14), and it is replaced by γέεννα (19:20; 20:10, 14 f.: λίμνη τοῦ πυρός) as the final place of punishment."
This quotation is followed by a description of variations on details in the NT, with Luke 16 seeing Hades as having both saved and unsaved (though with their experiences being very different), and in other cases the saved go immediately to Paradise.
[Joachim Jeremias, in TDNT]
To my knowledge, this is a consensus position among NT scholars. Hence Luke 16 is describing Hades, not the final judgement.
[There is also an article in TDNT on Gehenna, also by Jeremias. But it's briefer, and only speaks of being "destroyed by eternal fire." I assume he intends the usual meaning of destroyed, but I guess you can't be sure he doesn't mean destroyed in the sense of being tormented. Unfortunately there's really not enough detail in that article to be very helpful. So far I haven't found any good treatment of the history of the concept of Gehenna, and its likely NT meaning.]